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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2402.12643 |
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| _version_ | 1866913879459627008 |
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| author | Kulp, Isaac Ochanine, Charlotte Richard, Logan Robert, Leonel Whitman, Scott |
| author_facet | Kulp, Isaac Ochanine, Charlotte Richard, Logan Robert, Leonel Whitman, Scott |
| contents | We call a continuous path of polygons decreasing if the convex hulls of the polygons form a decreasing family of sets. For an arbitrary polygon of more than three vertices, we characterize the polygons contained in it that can be reached by a decreasing path (attainability problem), and we show that this can be done by a finite application of "pull-in" moves (bang-bang problem). In the case of triangles, this problems was investigated by Goodman, Johansen, Ramsey, and Frydman among others, in connection with the embeddability problem for non-homogeneous Markov processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decreasing paths of polygons Kulp, Isaac Ochanine, Charlotte Richard, Logan Robert, Leonel Whitman, Scott Metric Geometry Probability 52A10, 60J27, 52C45 We call a continuous path of polygons decreasing if the convex hulls of the polygons form a decreasing family of sets. For an arbitrary polygon of more than three vertices, we characterize the polygons contained in it that can be reached by a decreasing path (attainability problem), and we show that this can be done by a finite application of "pull-in" moves (bang-bang problem). In the case of triangles, this problems was investigated by Goodman, Johansen, Ramsey, and Frydman among others, in connection with the embeddability problem for non-homogeneous Markov processes. |
| title | Decreasing paths of polygons |
| topic | Metric Geometry Probability 52A10, 60J27, 52C45 |
| url | https://arxiv.org/abs/2402.12643 |